NEW YORK (CNN) -- After declaring last week that he won't publicly discuss his sexual relationships with staffers again, David Letterman continued his mea culpa Monday night -- saying his wife had been "horribly hurt by my behavior."

David Letterman has mined private events in his life for very public jokes on his show.

The host of CBS' "Late Show" said he now has to try to repair his relationship with Regina Lasko.

"Either you're going to make some progress and get it fixed, or you're going to fall short and perhaps not get it fixed, so let me tell you folks, I got my work cut out for me," he told the audience.

The words came about 15 minutes into the show, but Letterman fired self-deprecating zinger after zinger as soon as he strode on stage and began his opening monologue. Watch Letterman's apology to his wife »

"I mean, I'll be honest with you folks," he said. "Right now, I would give anything to be hiking on the Appalachian Trail. I got in the car this morning -- and the navigation lady wasn't speaking to me."

Letterman added it was fall in the city and that he spent the weekend "raking my hate mail."

Don't Miss

Monday's show was the first that Letterman had taped since he announced Thursday night that he had sex with unnamed members of his staff and had testified about those liaisons before a New York grand jury as part of an alleged extortion attempt.

A CBS producer, Robert "Joe" Halderman, is accused of threatening to go public with embarrassing information about Letterman's private life, unless the 62-year-old funnyman ponied up $2 million.

While prosecutors did not reveal where Halderman may have gotten information about Letterman's private life, one of the comedian's assistants, identified by Halderman family members and court documents as Stephanie Birkitt, was once the suspect's live-in girlfriend.

A highly placed source close to Letterman told CNN that Birkitt was one of the female staffers involved in sexual relationships with the comedian.

"Last week on the show, I told a little story about being blackmailed. I wasn't going to talk about it anymore, but seems like people want to talk about it," he said as he began his apology in earnest.

"The staff here has been wonderfully supportive to me, not just through this furor, but through all the years that we've been on television. ... So, again, my thanks to the staff for, once again, putting up with something stupid I've gotten myself involved in," he continued.

Then he addressed Lasko, whom he began dating in 1986. The couple married in March and have a 5-year-old son together. All the affairs took place before the marriage, Letterman's production company has said.

"Now the other thing is my wife, Regina. She has been horribly hurt by my behavior, and when something happens like that, if you hurt a person and it's your responsibility, you try to fix it."

The show, which airs at 11:30 p.m. ET, is taped earlier in the day.

Larry Lefkowitz of Brooklyn Heights, New York, who attended the taping, found Letterman's apology sincere.

"You could tell he'd been though a difficult situation and that he was sorry that he hurt other people, but he was also able to keep it funny, throw humor into it, too," Lefkowitz said.

Richard Zoglin, an editor at Time magazine and author of "Comedy at the Edge: How Standup in the 1970s Changed America," said he wasn't surprised by Letterman letting the scandal play out in public.

"David, of course, is a very private person. But it's not surprising in the sense that, over the years, what's made David Letterman a fascinating TV personality is how he's allowed us these little peeks into his private life and he's become a more human sort of person, not Mr. Irony, as he started out to be," Zoglin said on "Larry King Live." Watch panel discuss Letterman on "Larry King Live" »

"I think that this is just another peek inside the real David Letterman. And it's making him kind of even more fascinating than before."

The suspect in the case, Robert "Joe" Halderman of Norwalk, Connecticut, is a 27-year CBS veteran, most recently a producer for the network's news magazine "48 Hours."

He pleaded not guilty Friday to charges of first-degree attempted grand larceny and has been suspended from his job. If convicted, the 51-year-old could face up to 15 years in prison.

Halderman's lawyer, Gerald Shargel, told NBC's "Today" show Monday that Letterman's self-disclosure is not the only version of events.

"David Letterman didn't give his side of the story. David Letterman gave what he wanted the public to know," Shargel said.

"He wanted to get out ahead of the story and that's exactly what he did. He's a master of manipulating audiences. That's what he does for a living. So to think that David Letterman gave the entire story and there's nothing more to be said is simply wrong."

The flood of attention on the "sextortion" revelations -- as they have come to be called -- is unlikely to die down soon, Letterman acknowledged Monday night.

"Ladies and gentleman, this is only phase one of the scandal," he joked. "Phase two? Next week I go on 'Oprah' and sob."